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Greedoids (Hardcover)
Loot Price: R2,843
Discovery Miles 28 430
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Greedoids (Hardcover)
Series: Algorithms and Combinatorics, Vol 4
Expected to ship within 12 - 17 working days
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Total price: R2,863
Discovery Miles: 28 630
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I. Introduction.- 1. Set Systems and Languages.- 2. Graphs,
Partially Ordered Sets and Lattices.- II. Abstract Linear
Dependence - Matroids.- 1. Matroid Axiomatizations.- 2. Matroids
and Optimization.- 3. Operations on Matroids.- 4. Submodular
Functions and Polymatroids.- III. Abstract Convexity -
Antimatroids.- 1. Convex Geometries and Shelling Processes.- 2.
Examples of Antimatroids.- 3. Circuits and Paths.- 4. Helly's
Theorem and Relatives.- 5. Ramsey-type Results.- 6. Representations
of Antimatroids.- IV. General Exchange Structures - Greedoids.- 1.
Basic Facts.- 2. Examples of Greedoids.- V. Structural Properties.-
1. Rank Function.- 2. Closure Operators.- 3. Rank and Closure
Feasibility.- 4. Minors and Extensions.- 5. Interval Greedoids.-
VI. Further Structural Properties.- 1. Lattices Associated with
Greedoids.- 2. Connectivity in Greedoids.- VII. Local Poset
Greedoids.- 1. Polymatroid Greedoids.- 2. Local Properties of Local
Poset Greedoids.- 3. Excluded Minors for Local Posets.- 4. Paths in
Local Poset Greedoids.- 5. Excluded Minors for Undirected
Branchings Greedoids.- VIII. Greedoids on Partially Ordered Sets.-
1. Supermatroids.- 2. Ordered Geometries.- 3. Characterization of
Ordered Geometries.- 4. Minimal and Maximal Ordered Geometries.-
IX. Intersection, Slimming and Trimming.- 1. Intersections of
Greedoids and Antimatroids.- 2. The Meet of a Matroid and an
Antimatroid.- 3. Balanced Interval Greedoids.- 4. Exchange Systems
and Gauss Greedoids.- X. Transposition Greedoids.- 1. The
Transposition Property.- 2. Applications of the Transposition
Property.- 3. Simplicial Elimination.- XI. Optimization in
Greedoids.- 1. General Objective Functions.- 2. Linear Functions.-
3. Polyhedral Descriptions.- 4. Transversals and Partial
Transversals.- 5. Intersection of Supermatroids.- XII. Topological
Results for Greedoids.- 1. A Brief Review of Topological
Prerequisites.- 2. Shellability of Greedoids and the Partial Tutte
Polynomial.- 3. Homotopy Properties of Greedoids.- References.-
Notation Index.- Author Index.- Inclusion Chart (inside the back
cover).
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